Simulation of the temperature distribution of lithium-ion battery module considering the time-delay effect of the porous electrodes

The porous electrodes have the fractal characteristics of self-similarity and discontinuity at the microscopic scale, which is an important physical condition in the fractional-order system. During the charging and discharging, the multiple heat transfer modes occur simultaneously on the porous electrodes. Due to the different heat transfer rates of various modes, the thermodynamics of batteries is essentially a discontinuous time-delay system, which cannot be ignored. A fractional-order heat transfer model (FOHTM) is proposed to analyze the time-delay effect of the lithium-ion battery module. The fractional derivative order (FDO) of the proposed model is identified. The temperature distribution of the tested battery module is simulated and the cooling system is optimized. The results indicate that the simulation accuracy of FOHTM is higher than that of the classical integer-order heat transfer model (IOHTM). The maximum error of transient temperature of FOHTM under various operating conditions is less than 1.1%. The FOHTM can approach the true temperature faster through updating the historical weighted terms. The FOHTM is a statistical analysis of non-standard thermal diffusion behavior under the action of multiple heat transfer modes, as a result of which, it is more suitable for the modeling of battery thermodynamics.